A cyclist rides 55km on a bearing of 010° to town Y, and from there, he rides 65km on a bearing of 100° to town Z. Find the distance XZ.

Here are the solutions to the problems involving bearings and distances.

: A cyclist rides 55km on a bearing of $010^\circ$ to town Y, and from there, he rides 65km on a bearing of $100^\circ$ to town Z.

a) Find the distance XZ.
Let X be the starting point. We have a triangle XYZ with sides XY = 55 km and YZ = 65 km. We need to find the angle $\angle XYZ$.
The bearing from X to Y is $010^\circ$.
The bearing from Y to Z is $100^\circ$.
Draw a North line at Y. The angle between the North line at Y